• Measuring, quantifying, and keeping record of our social and natural environments.
• Keep track of time, seasons.
• Property rights: define/quantify land areas.
• Quantify harvest/yield.

More advanced economy:

• More sophisticated division of labor
• More complex property rights
• More need to keep track of everything.

More advanced economy: more data to handle

• How to keep track of calculations with large numbers?
• Mechanical aids: pebbles, shells, etc.
• Devices: invention of the counting frame ('abacus')

How does the abacus work?

• Need to agree on a standard (numeral system)!
• Define the base of the frame's numeral system.
• For example, a Roman abacus with base 10.

The example in more detail:

• Columns reflect the positions of the digits
• and signify the power of 10 which which the digit is multiplied:

\(139=(1 \times 10^{2}) + (3 \times 10^{1}) + (9 \times 10^{0})\)

• Base 10: 10 different signs (0-9) to distinguish one-digit numbers.

• What we work with in everyday life.
• What we encounter in undergraduate math, statistics, etc.
• However, not the relevant base once we use electronic tools.

Microprocessors can only represent two signs (states):

• 'Off' = 0
• 'On' = 1

• Only two signs: 0, 1.
• Base 2.
• Columns: \(2^0=1\), \(2^1=2\), \(2^3=4\), and so forth.

• Sufficient to represent all natural numbers in the decimal system.
• Representing fractions is tricky
  • e.g. \(1/3=1.333..\) actually constitutes an infinite sequence of 0s and 1s.
  • Solution: 'floating point numbers' (not 100% accurate)

What is the decimal number 139 in the binary counting frame?

What is the decimal number 139 in the binary counting frame?

• Solution:

\[(1 \times 2^7) + (1 \times 2^3) + (1 \times 2^1) + (1 \times 2^0) = 139.\]

What is the decimal number 139 in the binary counting frame?

• Solution:

\[(1 \times 2^7) + (1 \times 2^3) + (1 \times 2^1) + (1 \times 2^0) = 139.\]

• More precisely:

\[(1 \times 2^7) + (0 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (1 \times 2^3)\\ + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 139.\]

• That is, the number 139 in the decimal system corresponds to 10001011 in the binary system.

If computers only understand 0 and 1, how can they express decimal numbers like 139?

If computers only understand 0 and 1, how can they express decimal numbers like 139?

• Standards define how symbols, colors, etc are shown on the screen.
• Facilitates interaction with a computer (our keyboards do not only consist of a 0/1 switch).

• Binary numbers can become quite long rather quickly.
• Computer Science: refer to binary numbers with the hexadecimal system.

• Binary numbers can become quite long rather quickly.
• Computer Science: refer to binary numbers with the hexadecimal system.

• 16 symbols:

• 0-9 (used like in the decimal system)…

• and A-F (for the numbers 10 to 15).

• 16 symbols: base 16: each digit represents an increasing power of 16 (\(16^{0}\), \(16^{1}\), etc.).

What is the decimal number 139 expressed in the hexadecimal system?

What is the decimal number 139 expressed in the hexadecimal system?

• Solution: \[(8\times 16^1) + (11\times 16^0) = 139.\]

What is the decimal number 139 expressed in the hexadecimal system?

• Solution: \[(8\times 16^1) + (11\times 16^0) = 139.\]

• More precisely: \[(8\times 16^1) + (B\times 16^0) = 8B = 139.\]

What is the decimal number 139 expressed in the hexadecimal system?

• Solution: \[(8\times 16^1) + (11\times 16^0) = 139.\]

• More precisely: \[(8\times 16^1) + (B\times 16^0) = 8B = 139.\]

• Hence: 10001011 (in binary) = 8B (in hexadecimal) = 139 in decimal.

Advantages (when working with binary numbers)

1. Shorter than raw binary representation
2. Much easier to translate forth and back between binary and hexadecimal than binary and decimal.

Advantages (when working with binary numbers)… Why?

• Hexadecimal digits can always be represented in four-digit binary equivalent.
• \(8=1000\), \(B=11=1011\), thus…
• 8B (in hexadecimal) = 10001011 (1000 1011) in binary.

How can a computer understand text if it only understands 0s and 1s?

A modified version of South Korean Dubeolsik (two-set type) for old hangul letters. (Illustration by Yes0song 2010, Creative Commons Attribution-Share Alike 3.0 Unported)

How can a computer understand text if it only understands 0s and 1s?

• Standards define how 0s and 1s correspond to specific letters/characters of different human languages.
• These standards are usually called character encodings.
• Coded character sets that map unique numbers (in the end in binary coded values) to each character in the set.
• For example, ASCII (American Standard Code for Information Interchange).

ASCII logo. (public domain).

• In practice, Data Science means handling digital data of all formats and shapes.
  • Diverse sources.
  • Different standards.
  • read/store data.
• At the lowest level, this means understanding/handling encodings.

Two core themes of this course:

1. How can data be stored digitally and be read by/imported to a computer?
2. How can we give instructions to a computer by writing computer code?

Two core themes of this course:

1. How can data be stored digitally and be read by/imported to a computer?
2. How can we give instructions to a computer by writing computer code?

In both of these domains we mainly work with one simple type of document: text files.

• A collection of characters stored in a designated part of the computer memory/hard drive.
• A easy to read representation of the underlying information (0s and 1s)!
• Common device to store data:
  • Structured data (tables)
  • Semi-structured data (websites)
  • Unstructured data (plain text)
• Typical device to store computer code.

Install RStudio from here!

Install Atom from here!

Recall the initial example (survey) of this course.

1. Access a website (over the Internet), use keyboard to enter data into a website (a Google sheet in that case).

2. R program accesses the data of the Google sheet (again over the Internet), download the data, and load it into RAM.

3. Data processing: produce output (in the form of statistics/plots), output on screen.

Download the website (read its source code into RAM)

clockHTML <- readLines("https://www.census.gov/popclock/")

Have a look at the first lines of the webpage's source code:

head(clockHTML)

## [1] "<!DOCTYPE html PUBLIC \"-//W3C//DTD XHTML 1.0 Transitional//EN\""
## [2] "   \"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd\">" 
## [3] "<html lang=\"en\">"                                              
## [4] "<head>"                                                          
## [5] "\t<title>Population Clock</title>"                               
## [6] "        <meta charset=\"UTF-8\">"

Search the source code for the line that contains the part of the website with the world population counter:

line_number <- grep('id="world-pop-container"', clockHTML)

We can now check on which line the text was found.

line_number

## [1] 4611

writeLines(clockHTML, "clock.html")